sum from n=0 to infinity of 5/(8^n)

解答

n = 0 \sum \infty \frac{5}{8 ^{n}}

\frac{40}{7}

十进制

5.71428 \dots

求解步骤

n = 0 \sum \infty \frac{5}{8 ^{n}}

使用常数相乘法则:

\sum c \cdot a_{n} = c \cdot \sum a_{n}

= 5 \cdot n = 0 \sum \infty \frac{1}{8 ^{n}}

使用几何级数审敛法:

\frac{8}{7}

= 5 \cdot \frac{8}{7}

化简

5 \cdot \frac{8}{7} : \frac{40}{7}

= \frac{40}{7}

n = 2 \sum \infty \frac{1}{n ^{0} ln ( n )}

k = 1 \sum \infty (cos (1))^{k}

n = 3 \sum \infty \frac{2 n}{n + 2}

k = 2 \sum \infty (- 0.65)^{k}

n = 2 \sum \infty (\frac{3}{7})^{2 n}